On the Convergence of the Electronic Structure Properties of the FCC
Americium (001) Surface
Da Gao and Asok K. Ray*
Department of Physics
P. O. Box 19059
University of Texas at Arlington
Arlington, Texas 76019
*[email protected].
Abstract
Electronic and magnetic properties of the fcc Americium (001) surface have been
investigated via full-potential all-electron density-functional electronic structure
calculations at both scalar and fully relativistic levels. Effects of various theoretical
approximations on the fcc Am (001) surface properties have been thoroughly examined.
The ground state of fcc Am (001) surface is found to be anti-ferromagnetic with spinorbit coupling included (AFM-SO). At the ground state, the magnetic moment of fcc Am
(001) surface is predicted to be zero. Our current study predicts the semi-infinite surface
energy and the work function for fcc Am (001) surface at the ground state to be
approximately 0.82 J/m2 and 2.93 eV respectively. In addition, the quantum size effects
of surface energy and work function on the fcc Am (001) surface have been examined up
to 7 layers at various theoretical levels. Results indicate that a three layer film surface
model may be sufficient for future atomic and molecular adsorption studies on the fcc
Am (001) surface, if the primary quantity of interest is the chemisorption energy.
Keywords: Actinides; Americium; Electronic Structure; Surface Properties; Density
Functional Theory
PACS: 71.15.-m; 71.27+a; 73.20.At; 75.50.Ee.
I. Introduction
Actinides, the elements from actinium and beyond in the periodic table including
uranium, plutonium, americium and other radioactive elements, are well-known nuclear
weapon materials. In as much as they are praised for their role in ending the Cold War,
understandable concerns persist about their potentially catastrophic impact on the
environment and global health [1]. On the scientific front, the miraculous 5f electron
properties of the actinides, being strongly correlated and heavy fermion systems,
especially their bonding properties, are still not well understood because of their inherent
complexities. To address these issues, a significant amount of theoretical study is
required since experimental work is relatively difficult to perform on actinides due to
material problems and toxicity. Moreover, such studies are essential for the actinides’
rational use, safe disposition, and reliable long-term storage.
In the actinides, americium occupies a pivotal position with regard to the 5f electron
properties [2]. First, although the atomic volume of the actinides before Pu continuously
decreases as a function of the increasing atomic number from Ac until Np, a sharp atomic
volume increase from Pu to Am has been observed [3]. Such observation indicates that
the 5f electron properties have changed dramatically starting from somewhere between
Pu and Am. It is believed that the 5f electrons of the actinides before Am are delocalized
and participate in bonding while the 5f electrons of the actinides after Pu become
localized and non bonding [4, 5]. Our earlier fully relativistic density functional studies
of the fcc Am bulk and the Am monolayer properties, using both local density and
generalized gradient approximations, as well as other published works in the literature
have supported the localized picture for Am [6-8]. Second, as the applied pressure is
increased, the americium metal displays different crystal structures [9]: double hexagonal
close packed (Am I) → face-centered cubic (Am II) → face-centered orthorhombic (Am
III) → primitive orthorhombic (Am IV). Such behaviors could further provide more
insights of the americium 5f electron properties, especially the Mott transition, i.e., the
evolution of the 5f electrons from localized to the delocalized. The experimental studies
have shown that the 5f electrons of Am III and Am IV are probably delocalized [2, 9].
However, recent density-functional electronic structure calculations with respect to the
high-pressure behavior of americium found only the fourth phase (Am IV) to be
delocalized and the 5f electrons of the three previous americium phases to be primarily
localized [10]. Such controversies clearly indicate that further experimental and
theoretical studies are required to improve our understanding of americium and the
associated 5f electrons. Third, the electronic structure of americium metal, whereby six f
electrons form an inert core, decoupled from the spd electrons that control the physical
properties of the material, have contributed to superconductivity in Am [11, 12]. A recent
high-pressure study of the resistivity of americium metal has been reported and deduced
the unusual dependence of the superconducting temperature on pressure [13].
However, to the best of our knowledge, very few studies exist in the literature about
the Am surface despite the fact that such surface studies may lead to a better
understanding of the detailed americium surface corrosion mechanisms in the presence of
environmental gases and thus help addressing the environmental consequences of nuclear
materials. Moreover, surface studies may provide an effective way to probe the
americium 5f electron properties and their roles in the chemical bonding. The unusual
aspects of the bonding in bulk americium are apt to be enhanced at a surface or in a thin
layer of americium adsorbed on a substrate as a result of the reduced atomic coordination
of a surface atom and the narrow bandwidth of surface states. Thus, americium surfaces
and thin films may also provide valuable information about the bonding in americium.
Recently, Gouder et al. have studied thin films of Am, AmN, AmSb, and Am2O3
prepared by sputter deposition by x-ray and ultraviolet photoelectron spectroscopy (XPS
and UPS) techniques. Their experimental studies indicate that in all four Am systems, 5f
electrons are largely localized, though the XPS core-level spectrum of Am indicates
residual 5f hybridization [14].
We have recently investigated, in detail, the surface properties of fcc δ–Pu and
atomic and molecular adsorptions on such surfaces [15]. At the same time, we are also
particularly intrigued by the surface properties of Am, the nearest neighbor of Pu. Both
Pu and Am represent the boundary position between the light actinides, Th to Pu, and the
heavy actinides, Am and beyond. Pu has an open shell of f electrons while Am is closer
to a full j = 5/2 shell. In addition, the transition from the itinerant to localized 5f electrons
takes place somewhere between Pu and Am; yet there is no such apparent transition
observed, at least, in α-Pu although the 5f electrons of δ-Pu are partially localized [16], as
indicated by its atomic volume, which is approximately halfway between α-Pu and Am.
Thus we believe systematic and fully relativistic density functional studies of Pu and Am
surface chemistry and physics could certainly lead to more insights and knowledge about
the actinides.
In this paper, for the first time we report on the fcc Am (001) surface properties and a
detailed comparison with the published fcc δ-Pu (001) surface properties. For such
surface studies, it is common practice to model the surface of a semi-infinite solid with an
ultra thin film (UTF), which is thin enough to be treated with high-precision densityfunctional calculations, but is thick enough to realistically model the intended surface.
Determination of an appropriate UTF thickness is complicated by the existence of
possible quantum oscillations in UTF properties as a function of thickness, the so-called
quantum size effect (QSE). These oscillations were first predicted by calculations on
jellium films [17, 18] and were subsequently confirmed by band-structure calculations on
free-standing UTFs composed of discrete atoms [19-22]. The adequacy of the UTF
approximation obviously depends on the size of any QSE in the relevant properties of the
model film. Thus, it is important to determine the magnitude of the QSE in a given UTF
prior to using that UTF as a model for the surface. This is particularly important for Am
films, since the strength of the QSE is expected to increase with the number of valence
electrons [17]. Consequently, this study has also examined the QSE of the fcc Am (001)
surface.
II. Computations
The present calculations have been carried out using the full-potential all-electron
method with a mixed basis set of
linearized-augmented-plane-wave (LAPW) and
augmented-plane-wave plus local orbitals (APW+lo), with and without spin-orbit
coupling (SO), as implemented in the WIEN2K suite of programs [23-25]. Six theoretical
levels of approximation, i.e., anti-ferromagnetic-no-spin-orbit-coupling (AFM-NSO),
anti-ferromagnetic-spin-orbit-coupling (AFM-SO), spin-polarized-no-spin-orbit-coupling
(SP-NSO), spin-polarized-spin-orbit-coupling (SP-SO), non-spin-polarized-no-spin-orbitcoupling (NSP-NSO), and non-spin-polarized-spin-orbit-coupling (NSP-SO) have been
implemented in our calculations. The generalized-gradient-approximation (GGA) to
density functional theory [26] with a gradient corrected Perdew- Berke - Ernzerhof (PBE)
exchange-correlation functional [27] is used and the Brillouin-zone integrations are
conducted by an improved tetrahedron method of Blöchl-Jepsen-Andersen [28]. In the
WIEN2k code, the alternative basis set APW+lo is used inside the atomic spheres for the
chemically important orbitals that are difficult to converge, whereas LAPW is used for
others. The local orbitals scheme leads to significantly smaller basis sets and the
corresponding reductions in computing time, given that the overall scaling of LAPW and
APW + lo is given by N3, where N is the number of atoms. In addition, results obtained
with the APW + lo basis set converge much faster and often more systematically towards
the final value [29]. As far as relativistic effects are concerned, core states are treated
fully relativistically in WIEN2k and for valence states, two levels of treatments are
implemented: (1) a scalar relativistic scheme that describes the main contraction or
expansion of various orbitals due to the mass-velocity correction and the Darwin s-shift
[30] and (2) a fully relativistic scheme with spin-orbit coupling included in a second
variational treatment using the scalar-relativistic eigenfunctions as basis [31]. The present
computations have been carried out at both scalar-relativistic and fully-relativistic levels
to determine the effects of relativity. To calculate the total energy, a constant muffin-tin
radius (R
mt)
of 2.60 a.u. is used for all calculations. The plane-wave cut-off K
cut
is
determined by Rmt Kcut = 9.0. The (001) surface of fcc Am is modeled by periodically
repeated slabs of N Am layers (with one atom per layer and N=1-7) separated by an 80 a.
u. vacuum gap. We have tested different vacuum gap lengths in order to determine an
appropriate length such that an accurate result can be achieved without an excessive
increase in computational costs. Twenty-one irreducible K points have been used for
reciprocal-space integrations. For each calculation, the energy convergence criterion is
set to be 0.01 mRy. Due to severe demands on computational resources due to allelectron calculations and internal consistency, we have chosen the calculated equilibrium
lattice constants, obtained at different levels of approximation for bulk fcc Am [6], also in
the surface computations at the corresponding level of approximation. No further
relaxations and/or reconstructions have been taken into account. It is not expected that
this will change the primary conclusions of this paper.
III. Results and Discussions
We first calculated the total energies for fcc Am (001) films at all six theoretical levels,
namely NSP-NSO, NSP-SO, SP-NSO, SP-SO, AFM-NSO, and AFM-SO levels, and
plotted the results in Fig. 1, respectively. For comparison, the total energies of the fcc Am
bulk at the corresponding theoretical level are also plotted in Fig. 1. Our results showed
that with spin orbit coupling, the total energies of fcc Am (001) films are much lower,
about 0.60 Ry/atom, than those without spin orbit coupling, as has been observed also
before in the bulk properties. A similar spin polarization effect on the total energies of
Am (001) films is found here with or without the inclusion of spin orbit coupling effects.
From the total energy point of view, the Am (001) films at the AFM-SO level have the
lowest total energy and therefore the AFM-SO is the ground state of the Am (001) films,
which is consistent with the former theoretically predicted fcc Am bulk ground state [6,
10, 32], though the ground state of Am is experimentally believed to be nonmagnetic [8].
In our previous electronic structure studies [15] of bulk δ-Pu and the δ-Pu surfaces, the
ground state is also found to be AFM-SO.
We also calculated the cohesive energies E coh for the fcc Am (001) N-layer films
with respect to N monolayers and found that the cohesive energy increases monotonously
with the film thickness (shown in Fig. 2 and Table I) at all six levels of calculations. It is
also observed that the rate of increase of cohesive energy drops significantly as the
number of layers increases, which has been previously noticed for the cohesive energy of
δ-Pu (001) surface as well, and we expect that the convergence in the cohesive energy
can be achieved after a few more layers. However, since to the best of our knowledge, the
experimental value for the semi-infinite surface cohesive energy is not known, we are
unable to predict how many layers will be needed to achieve the semi-infinite surface
energy. Typically, spin polarization lowers the cohesive energy by ~32%-50% at both the
scalar relativistic and fully relativistic levels of theory. On the other hand, spin-orbit
coupling increases the cohesive energy of the spin-polarized N-layers by about ~11-13%
but reduces the cohesive energy of the non-spin-polarized N-layers by about ~9-15%.
These features are in general agreement with the results of δ-Pu (001) surface [15]. At the
antiferromagnetic state, spin-orbit coupling increases the cohesive energy of the N-layers
by about ~13-15%. All cohesive energies are positive, indicating that all layers of Am
(001) films are bound relative to the monolayer.
The incremental energies Einc of N layers with respect to (N-1) layers plus a single
monolayer are also calculated and plotted (shown in Fig. 3 and Table I). The incremental
energies are found to become relatively stable when the number of layers is greater than
five. The study of the δ-Pu (001) films shows the incremental energies quickly saturated
once the number of δ-Pu (001) layers is greater than three [15]. We also notice that both
E coh and Einc of fcc Am (001) films are smaller than those of δ-Pu (001) films. Such
difference indicates that the layers of δ-Pu (001) films are strongly bound relative to the
monolayer, compared to layers of fcc Am (001) films. This is attributed to the 5f electron
properties of fcc Am and fcc δ-Pu, namely, that the 5f electrons are more localized in fcc
Am rather than in δ-Pu.
To further address the effects brought by the spin polarization and the spin-orbit
coupling, we also calculated spin-polarization energies and spin-orbit coupling energies
for the Am (001) films at various theoretical levels, and the results are shown in Table II
as well as in Fig. 4 and Fig. 5. The spin-polarization energy Esp is defined by
E SP = Etot ( NSP ) − Etot ( SP),
(1)
and the spin-orbit coupling energy Eso is defined by
E so = Etot ( NSO ) − Etot ( SO ),
(2)
We note that both spin polarization and spin orbit coupling energies become rather stable
when the number of layers equals three. It can also be seen that spin-orbit coupling plays
a more important role than spin-polarization in reducing the total energies of the fcc Am
(001) films, i.e., spin-orbit coupling effect reduces the total energy by 7.56-8.94 eV/atom,
while spin-polarization effect decreases the total energy only by 1.52-3.53 eV/atom.
Comparing these to the SO coupling and SP effects in the δ-Pu (001) films, which are
7.11-7.99 eV/atom and 0.4-1.9 eV/atom respectively [14], the effects in fcc Am (001)
films are more pronounced, especially the spin polarization effect. The discrepancy can
also be partially attributed to the additional 5f electron in Am and the localized feature of
these electrons.
As far as the magnetic properties of fcc Am (001) surface are concerned, the spin
magnetic moments of fcc Am (001) films at the SP-NSO, SP-SO, AFM-NSO, and AFM-
SO levels have been calculated and the results are listed in Table II. We also plotted these
magnetic moments for Am (001) films as a function of the number of Am layers in Fig.6.
Several features have been observed for the magnetic properties. First, for the Am (001)
films at both AFM-NSO and AFM-SO levels, the magnetic moments show a behavior of
oscillation, which becomes smaller with the increase of the number of layers, and
gradually the magnetic moments approach zero. The Am (001) films with an odd number
of layers have magnetic moments decreasing with the increase of the number of layers,
while the Am (001) films with an even number of layers always have zero magnetic
moments. Second, for the Am (001) films at the SP-NSO and SP-SO levels, the magnetic
moments are, in general, larger than the corresponding bulk values of 7.32 and 6.90
µ B /atom [6], and with the increase of the number of layers the magnetic moments
quickly approach the values of the corresponding bulks. For the seven layers thick film,
the magnetic moment at the SP-NSO and SP-SO levels is 7.32 and 6.95 µ B /atom already.
The spin magnetic moments of δ-Pu (001) films at the SP-NSO and SP-SO levels show a
similar feature as found here except that the magnetic moments of δ-Pu (001) films are
smaller than the corresponding magnetic moments of Am (001) films. The difference is
attributed to the additional 5f electron in Am. Third, for the Am (001) films at the antiferromagnetic state, spin-orbit coupling has negligible effects on the magnetic properties
while for the Am (001) films at the spin-polarized states, spin-orbit coupling lowers the
magnetic moments about 0.37 µ B /atom.
We also studied the quantum size effects in the fcc Am (001) films. The relevant
physical quantities if interest here are typically the surface energies and work functions.
We have calculated the surface energy for a N-layer film from [33]
E s = (1 / 2)[ Etot ( N ) − NE B ],
(3)
where Etot (N ) is the total energy of the N-layer slab and E B is the energy of the infinite
crystal. Assuming N is large enough and E tot (N ) and E B are known to infinite precision,
then Eq. (3) is exact. However, if the bulk and film calculations are not entirely consistent
with each other, then E s will linearly diverge with increasing N. Stable and internally
consistent estimates of E s and E B can, however, be extracted from a series of values of
Etot ( N ) via a linear least-squares fit to [34]
E tot ( N ) = E B N + 2 E s ,
(4)
To obtain an optimal result, the fit to Eq. (4) should only be applied to films which
include, at least, one bulk-like layer, i.e., N > 2. This fitting procedure has been
independently applied to the fcc Am (001) films at all six levels of theory, respectively.
Accordingly, six values of E B , i.e., -61041.70707, -61042.35104, -61041.89126, 61042.45788, -61041.89118, and -61042.46001 Ry, and six values of semi-infinite
surface energy E s , i.e., 1.56, 1.48, 0.69, 0.80, 0.73, and 0.82 J/m2, are derived for the Am
(001) films at the NSP-NSO, NSP-SO, SP-NSO, SP-SO, AFM-NSO, and AFM-SO
levels, respectively. We note that the semi-infinite surface energy decreases by about
forty seven percent from the NSP-NSO level to the AFM-SO level. The surface energy
for each film has been computed using the calculated N-layer total energy and
appropriate fitted bulk energy. We have listed the results in Table III and also plotted the
predicted surface energies as a function of the number of Am layers in Fig. 7. Several
features of the fcc Am (001) surface energies are notable from our results. First, for all
the theoretical levels except the NSP-SO level, the surface energy of Am (001) films
converges pretty well to the corresponding semi-infinite surface energy when the
number of layers reaches three. A similar behavior is also found in the δ-Pu (001) films
[15]. From these results, we infer that a three layer film surface model may be sufficient
for future atomic and molecular adsorption studies on the Am (001) surface, if the
primary quantity of interest is the chemisorption energy. Second, our results show that
spin polarization plays a more significant effect on the Am (001) surface energy than the
spin orbit coupling does. To be specific, spin polarization lowers the Am (001) surface
energy from ~1.5 J/m2 down to ~0.8 J/m2. Third, the surface energy of Am (001) films at
the ground state, i.e., AFM-SO level, is predicted to be about 0.82 J/m2.
The work function W of the Am (001) surface is calculated according to the
following formula
W = V0 − E F ,
(5)
where V0 is the Coulomb potential energy at the half height of the slab including the
vacuum layer and E F is the Fermi energy. We have calculated the work functions of Am
(001) films up to seven layers at all six theoretical levels, i.e., NSP-NSO, NSP-SO, SPNSO, SP-SO, AFM-NSO, and AFM-SO, respectively. The results are listed in Table III
and plotted in Fig. 8 as well. It can be observed that the work functions show some
oscillations at all six theoretical levels up to seven layers. This is different from the δ-Pu
(001) films where no significant work function oscillation was observed beyond five
layers [15]. Furthermore, no clear even-odd oscillatory pattern is shown here. The
current results indicate that at least a 7-layer film is necessary for any future adsorption
investigation that requires an adsorbate-induced work function shift. The work functions
of Am (001) films at seven layers are calculated to be 3.30, 3.28, 2.67, 2.78, 2.78, and
2.93 eV at the NSP-NSO, NSP-SO, SP-NSO, SP-SO, AFM-NSO, and AFM-SO levels,
respectively. These values are, in general, smaller than the work functions of δ-Pu (001)
films [15].
The 5f electrons in the fcc Am bulk are found to be primarily localized [2, 6, 9,
10]. However, the phase transition from fcc Am II to Am III is still controversial [2, 9,
10], as mentioned earlier. We thus explored the density of states (DOS) of 5f electrons in
fcc Am (001) films at the ground state (AFM-SO level) with various number of layers
(N=1, 4, 7) in order to learn how the 5f electron properties in the Am (001) thin films
change as a function of the number of layers. The results have been plotted in Fig. 9.
From the figure, we first note that the two 5f peaks, one below the Fermi level while the
other above the Fermi level, are well separated by a wide gap indicating that the 5f
electrons are localized. The gap width is about 2 eV for the present Am (001) surface
calculations, which is in good agreement with the gap width found in the bulk dhcp Am
[10] and bulk fcc Am [6]. In addition, as the thickness of the Am (001) thin films
increases, the center of the first peak appears to be moving away from the Fermi level,
signifying more localized 5f electrons, which is consistent with a recent photoemission
study of the electronic structure of pure Am and Am compounds films [14]. In contrast
to this, the thickness dependence of the degree of 5f electron delocalization in δ-Pu (001)
films is varying [15]. Our current results indicate that as Am (001) films become thicker,
the 5f electrons in the Am (001) films tend to behave more like the 5f electrons in the
bulk phase. On the contrary, the 5f electrons are much less localized in Am (001)
monolayer than in the bulk. This means more 5f electrons participate in chemical
bonding in Am (001) monolayer, implying that the relaxed lattice constants in Am (001)
monolayer should be smaller than that in Am bulk. Our previous study of the Am and Pu
monolayer properties [6, 35] have shown a compression phenomena of the monolayers,
which is in agreement with the present work.
IV. Conclusions
We have performed full-potential all-electron density-functional electronic
structure study of the fcc Am ultrathin (001) films at both scalar and fully relativistic
levels. Our present calculation provides the first electronic structure results for fcc Am
(001) surface.
In order to examine effects of various theoretical approximations
including spin-polarization and spin-orbit coupling, our current study has been carried out
at six theoretical levels, namely, NSP-NSO, NSP-SO, SP-NSO, SP-SO, AFM-NSO, and
AFM-SO. Our results show that the ground state of fcc Am (001) surface is the antiferromagnetic state with spin-orbit coupling included. At the ground state, the magnetic
moment of fcc Am (001) surface is zero, which is in good agreement with the zero
magnetic moment found in the ground state Am metal [6, 8]. Our results indicate that
spin polarization lowers the cohesive energy by ~32%-50% at both the scalar relativistic
and fully relativistic levels of theory. On the other hand, spin-orbit coupling increases the
cohesive energy of the spin-polarized N-layers by about ~11-13% but reduces the
cohesive energy of the non-spin-polarized N-layers by about ~9-15%. At the
antiferromagnetic state, spin-orbit coupling increases the cohesive energy of the N-layers
(001) Am films by about ~13-15%.
Our present results predict the semi-infinite surface energy and the work
function for fcc Am (001) surface at the ground state to be approximately 0.82 J/m2 and
2.93 eV respectively. The corresponding quantum size effects on the fcc Am (001) films
have also been investigated up to 7 layers at different theoretical levels. We found that at
least a 7-layer film surface model is necessary for any future fcc Am (001) surface
adsorption investigation that requires an adsorbate-induced work function shift. Fnally,
the 5f electrons in fcc Am (001) thin films are found to be more localized as the films
become thicker. In contrast to this, the thickness dependence of the degree of 5f electron
delocalization in δ-Pu (001) films is varying.
Acknowledgments
This work is supported by the Chemical Sciences, Geosciences and Biosciences
Division, Office of Basic Energy Sciences, Office of Science, U. S. Department of
Energy (Grant No. DE-FG02-03ER15409) and the Welch Foundation, Houston, Texas
(Grant No. Y-1525).
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190 (2003).
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Fermion Systems (Academic, San Diego, 1990); R. M. Dreialer and E. K. U. Gross,
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Functional Theory Recent Progress and New Directions (Plenum, New York, 1998).
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Perdew, K. Burke, and Y. Wang, Phys. Rev. B 54, 16533 (1996); J. P. Perdew in
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Table I. Cohesive energies E coh per atom with respect to the monolayer and incremental
energies Einc for fcc Am (001) N layers (N = 1-7) at all six theoretical levels.
N
2
3
4
5
6
7
Theory
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
E coh
Einc
(eV/atom)
(eV)
1.37
1.16
0.69
0.78
0.66
0.75
1.70
1.48
0.88
0.99
0.85
0.98
1.83
1.65
0.97
1.09
0.95
1.09
1.91
1.73
1.04
1.15
1.00
1.15
1.97
1.79
1.07
1.20
1.04
1.19
2.01
1.82
1.10
1.23
1.07
1.21
2.75
2.32
1.39
1.56
1.33
1.51
2.34
2.12
1.26
1.40
1.22
1.43
2.24
2.17
1.23
1.40
1.25
1.41
2.24
2.03
1.29
1.40
1.20
1.40
2.26
2.06
1.27
1.43
1.24
1.37
2.26
2.05
1.25
1.42
1.22
1.36
Table II. Magnetic moments MM per atom ( µ B /atom), spin polarization energies per atom
Esp , spin orbit coupling energies per atom Eso , for the Am (001) N layers (N=1-7).
N
1
2
3
4
5
6
7
Theory
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
MM
( µ B /atom)
Esp
E so
(eV/atom)
(eV/atom)
7.70
7.52
7.81
7.60
3.49
2.11
3.53
2.17
7.32
7.01
0
0
2.81
1.73
2.82
1.76
7.33
7.02
2.43
2.39
2.68
1.62
2.69
1.67
7.31
6.93
0
0
2.63
1.55
2.65
1.60
7.35
6.97
1.46
1.41
2.61
1.53
2.62
1.59
7.35
6.97
0
0
2.59
1.53
2.60
1.57
7.32
6.95
1.03
1.01
2.58
1.52
2.58
1.56
8.94
7.56
7.58
8.73
7.65
7.67
8.73
7.67
7.71
8.76
7.68
7.72
8.76
7.68
7.73
8.75
7.69
7.73
8.75
7.69
7.73
Table III. Work functions W (in eV) and surface energies (in J/m2) for fcc Am (001) N
layers (N=1-7).
N
1
2
3
4
5
6
7
Theory
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
W
Es
(eV)
( J / m2 )
3.32
3.15
2.70
2.80
2.77
2.86
3.37
3.34
2.71
2.80
2.78
2.90
3.36
3.31
2.69
2.85
2.80
2.91
3.31
3.28
2.66
2.80
2.78
2.96
3.33
3.31
2.68
2.82
2.79
2.89
3.36
3.27
2.67
2.81
2.80
2.96
3.30
3.28
2.67
2.78
2.78
2.93
2.11
1.76
0.75
0.88
0.80
0.93
1.65
1.55
0.68
0.79
0.73
0.85
1.56
1.51
0.68
0.79
0.73
0.82
1.57
1.42
0.70
0.80
0.72
0.81
1.58
1.46
0.69
0.81
0.73
0.81
1.57
1.47
0.68
0.80
0.73
0.82
1.56
1.48
0.69
0.80
0.73
0.82
List of figures
Fig.1. Total energies of Am (001) films for different number of layers (N = 1 - 7). For
comparison, the corresponding total energies of Am bulk are also plotted at the farthest
right of the figure.
Fig.2. Cohesive energies per atom of the fcc Am (001) films with respect to the Am
monolayer versus the number of Am layers.
Fig.3. Incremental energies per atom of the fcc Am (001) films with respect to the (N-1)
fcc Am films plus the monolayer versus the number of Am layers
Fig.4. Spin-polarization energies (eV/atom) as a function of the number of Am layers for
Am (001) films for N layers (N=1-7).
Fig.5. Spin-orbit coupling energies (eV/atom) as a function of the number of Am layers
for Am (001) films for N layers (N=1-7).
Fig.6. Spin magnetic moments of the fcc Am (001) films for different layers (N=1-7).
Fig.7. Surface energies for the fcc Am (001) films vs. the number of Am layers.
Fig.8. Work functions of the fcc Am films (eV) vs. the number of Am (001) layers.
Fig.9. Density of states of 5f electrons for Am (001) N-layer films at the ground state,
where N = 1, 4, 7 as labeled in the figure. Fermi energy is set at zero.
-61041.8
-61041.5
-61041.50
-61042.1
-61042.15
NSP-NSO
SP-NSO
SP-NSO
AFM-NSO
-61041.8
-61041.6
-61041.5
-61041.55
NSP-SO
SP-SO
AFM-SO
-61042.2
-61042.20
-61042.2
-61042.25
-61041.6
-61041.8
-61041.6
-61041.65
Total Energy (Ry/atom)
Total Energy (Ry/atom)
-61041.8
-61041.6
-61041.6
-61041.60
-61041.8
-61041.6
-61041.8
-61041.7
-61041.70
-61041.8
-61041.6
-61041.7
-61041.75
-61041.9
-61041.7
-61042.3
-61042.30
-61042.3
-61042.35
-61042.4
-61042.40
-61041.9
-61041.8
-61041.80
-61041.7
-61041.9
-61042.4
-61042.45
-61041.8
-61041.85
-61041.7
-61041.9
-61041.7
-61041.9
-61041.90
1 11 2 22 3 333 4 44 5 55 6 666 777 8
Number
Numberof
ofAm
AmLayers
Layers
-61042.5
-61042.50
11
22
33
44
55
Number
Numberof
ofAm
AmLayers
Layers
Fig. 1. Total energies of Am (001) films for different number of layers (N = 1 - 7). For
comparison, the corresponding total energies of Am bulk are also plotted at the farthest
right of the figure.
66
7
2.2
AFM-SO
AFM-NSO
SP-SO
SP-NSO
2
NSP-SO
NSP-NSO
Cohesive Energy (eV)
1.8
1.6
1.4
1.2
1
0.8
0.6
2
3
4
5
Number of Am layers
6
Fig. 2. Cohesive energies per atom of the fcc Am (001) films with respect to the Am
monolayer versus the number of Am layers.
7
2.8
AFM-SO
AFM-NSO
SP-SO
SP-NSO
NSP-SO
NSP-NSO
2.6
Incremental Energy (eV)
2.4
2.2
2
1.8
1.6
1.4
1.2
1
2
3
4
5
Number of Am layers
6
Fig. 3. Incremental energies per atom of the fcc Am (001) films with respect to the (N-1)
fcc Am films plus the monolayer versus the number of Am layers
7
AFM-SO
AFM-NSO
SP-SO
SP-NSO
Spin-polarization Energy (eV/atom)
3.5
3
2.5
2
1.5
1
2
3
4
Number of Am layers
5
6
Fig. 4. Spin-polarization energies (eV/atom) as a function of the number of Am layers for
Am (001) films for N layers (N=1-7).
7
9
AFM-SO
SP-SO
NSP-SO
Spin-orbit Coupling Energy (eV/atom)
8.8
8.6
8.4
8.2
8
7.8
7.6
7.4
1
2
3
4
Number of Am layers
5
6
Fig. 5. Spin-orbit coupling energies (eV/atom) as a function of the number of Am layers
for Am (001) films for N layers (N=1-7).
7
Spin Magnetic Moment (uB/atom)
8.0
AFM-NSO
AFM-SO
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1
2
3
4
5
6
7
Spin Magnetic Moment (uB/atom)
Number of Am Layers
7.7
SP-NSO
SP-SO
7.6
7.5
7.4
7.3
7.2
7.1
7.0
6.9
1
2
3
4
Number of Am Layers
5
6
Fig.6. Spin magnetic moments of the fcc Am (001) films for different layers (N=1-7).
7
2.2
NSP-NSO
NSP-SO
SP-NSO
SP-SO
AFM-NSO
AFM-SO
2
Surface Energy (J/m2)
1.8
1.6
1.4
1.2
1
0.8
0.6
1
2
3
4
Number of Am Layers
5
6
Fig. 7. Surface energies for the fcc Am (001) films vs. the number of Am layers.
7
AFM-SO
AFM-NSO
NSP-SO
NSP-NSO
SP-SO
SP-NSO
3.6
Work Function (eV)
3.4
3.2
3
2.8
2.6
1
2
3
4
Number of Am Layers
5
6
Fig. 8. Work functions of the fcc Am films (eV) vs. the number of Am (001) layers.
7
Fig. 9. Density of states of 5f electrons for Am (001) N-layer films at the ground state,
where N = 1, 4, 7 as labeled in the figure. Fermi energy is set at zero.